In various research fields such as hydrogeology, environmental science and energy engineering, geological formations with fractures are frequently encountered. Accurately characterizing these fractured media is of paramount importance when it comes to tasks that demand precise predictions of liquid flow and the transport of solute and energy within them. Since directly measuring fractured media poses inherent challenges, data assimilation (DA) techniques are typically employed to derive inverse estimates of media properties using observed state variables like hydraulic head, concentration, and temperature. Nonetheless, the considerable difficulties arising from the strong heterogeneity and non-Gaussian nature of fractured media have diminished the effectiveness of existing DA methods. In this study, we formulate a novel DA approach known as PEDL (parameter estimator with deep learning) that harnesses the capabilities of DL to capture nonlinear relationships and extract non-Gaussian features. To evaluate PEDL’s performance, we conduct two numerical case studies with increasing complexity. Our results unequivocally demonstrate that PEDL outperforms three popular DA methods: ensemble smoother with multiple DA (ESMDA), iterative local updating ES (ILUES), and ES with DL-based update (ESDL). Sensitivity analyses confirm PEDL’s validity and adaptability across various ensemble sizes and DL model architectures. Moreover, even in scenarios where structural difference exists between the accurate reference model and the simplified forecast model, PEDL adeptly identifies the primary characteristics of fracture networks.

Seawater intrusion poses a substantial threat to water security in coastal regions, where numerical models play a pivotal role in supporting groundwater management and protection. However, the inherent heterogeneity of coastal aquifers introduces significant uncertainties into model predictions, potentially diminishing their effectiveness in management decisions. Data assimilation (DA) offers a solution by incorporating various types of observational data to characterize these heterogeneous coastal aquifers. Traditional DA techniques, like ensemble smoother using the Kalman formula (ESK) and Markov chain Monte Carlo, face challenges when confronted with the non-linearity, non-Gaussianity, and high-dimensionality issues commonly encountered in aquifer characterization. In this study, we introduce a novel DA approach rooted in deep learning (DL), referred to as ESDL, aimed at effectively characterizing coastal aquifers with varying levels of heterogeneity. We systematically investigate a range of factors that impact the performance of ESDL, including the number and types of observations, the degree of aquifer heterogeneity, the structure and training options of the DL models, etc. Our findings reveal that ESDL excels in characterizing heterogeneous aquifers, particularly when faced with non-Gaussian conditions. Comparison between ESDL and ESK under different experimentation settings underscores the robustness of ESDL. Conversely, in certain scenarios, ESK displays noticeable biases in the characterizing results, especially when measurement data from nonlinear and discontinuous processes are used. To optimize the efficacy of ESDL, meticulous attention must be given to the design of the DL model and the selection of training options, which are crucial to ensure the universal applicability of this DA method.

A document by Chengji Shen. Click on the document to view its contents.

This study examines the occurrence of riparian lenses adjacent to partially penetrating rivers under the controlled conditions of a laboratory sand tank. Laboratory experiments and numerical modeling of the freshwater lens extent are used to provide physical verification (in light of limited examples of well-characterized field cases) of the analytical methodology, thereby evaluating the underlying assumptions. Parameter calibration and uncertainty analysis are applied to assess both the experimental conditions and the benefit of lens observations in applying the analytical approach. The experimental freshwater lens was reproduced by both analytical and numerical models, with the exception of small mismatches (between analytical results and measured data) in the lens thickness in the near-river region. These are most likely due to vertical flow effects that arise from the partial river penetration and saltwater inflows to the river bottom, and that are only partly accounted for in the analytical approach. Uncertainty analysis highlighted that accurate lens predictions based on the analytical method requires calibration to direct lens measurements; a similar finding from earlier studies of fully penetrating river conditions. Sensitivity analysis highlighted that the saltwater head boundary, freshwater and saltwater densities, and the aquifer depth below the riverbed (in descending order of sensitivity) are lthe most important factors in controlling freshwater lens occurrence and saltwater discharge. The results provide the first physical verification of the occurrence of stable riparian lenses adjacent to partially penetrating, gaining rivers, and verify a recent analytical solution for lens extent and saltwater discharge.

Previous studies of freshwater lenses in saline aquifers adjoining gaining rivers (“riparian lenses”) have so far considered only rivers that fully penetrate the aquifer, whereas in most cases, rivers are only partially penetrating. This paper presents a new methodology for obtaining the saltwater discharge and the shape of a steady-state, non-disperive riparian lens, where the river is partially penetrating, combining two previous analytical solutions. The resulting analytical solution is compared to numerical modelling results to assess assumptions and the methodology adopted to approximate the “turning effect”, which is the change in groundwater flow direction (horizontal to vertical) near the partially penetrating river. A range of conditions are analysed, constrained by parameters adopted previously for River Murray floodplains (Australia). Consistency between analytical and numerical results highlight the capability of the proposed analytical solution to predict the riparian lens geometry and saltwater discharge into partially penetrating rivers. The sensitivity analysis indicates that larger riparian lenses are produced adjacent to the deeper and wider rivers, as expected. The change in width or depth of the river has more influence on the saltwater discharge and the horizontal extent of the riparian lens (and less effect on the vertical extent of the lens adjacent to the river) for shallower and narrower rivers. This research highlights the utility of the new method and demonstrates that the assumption of a fully penetrating river likely leads to significant overestimation of the saltwater discharge to the river and the riparian lens horizontal extent and vertical depth.